Asked by Luca
Determine the volume of the solid obtained by rotating the region bounded by y= x - x^3, x = 0, x = 1 and the x - axis about the y-axis.
Answers
Answered by
oobleck
Using shells (cylinders) of thickness dx, we have
v = ∫[0,1] 2πrh dx
where r = x and h = y
v = ∫[0,1] 2πx(x-x^3) dx = 4π/15
v = ∫[0,1] 2πrh dx
where r = x and h = y
v = ∫[0,1] 2πx(x-x^3) dx = 4π/15
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